The dependence of chamber dynamics on chamber dimensions

One can learn something about the determinants of ventricular dimensions and dynamics from a simple spherical model. We have derived equations showing how isometric pressure, compliance, isometric P-V curves and viscous resistance to wall displacement depend on dimensions of a spherical chamber whose fibers adjust for a "normal" stretch at a particular point in the pump cycle. The derivations show: (a) that isometric pressure at this point is proportional to the logarithm of total chamber volume (cavity plus wall) relative to cavity volume; (b) that compliance at this point is proportional to cavity volume and to total chamber volume relative to wall volume; (c) that the rate of wall displacement relative to the disparity between isometric pressure and actual pressure depends on dimensions like compliance depends on dimensions; and (d) since reciprocal compliance does not increase with wall/cavity ratios as much as isometric pressure at the normal-stretch volume, the P-V curves spread out on either side of the normal-stretch volume as the chamber undergoes adaptive thickening, resulting in disproportionate increases of isometric pressure at low cavity volumes. This tends to increase ejection fraction and reduce cavity volumes relative to stroke volume, and it is partly responsible for the "concentric" character of hypertrophy in response to high systolic pressure.